Use the properties of 30-60-90 and 45-45-90 triangles to solve for x in each of the problems below. Then decode the secret message by matching the answer with the corresponding letter/symbol from the exercises.
Answers
The trigonometric function gives the ratio of different sides of a right-angle triangle. The given problems can be solved as given below.
What are Trigonometric functions?The trigonometric function gives the ratio of different sides of a right-angle triangle.
[tex]\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\\\\\\Cosec \theta=\dfrac{Hypotenuse}{Perpendicular}\\\\\\Sec \theta=\dfrac{Hypotenuse}{Base}\\\\\\Cot \theta=\dfrac{Base}{Perpendicular}\\\\\\[/tex]
where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite to the 90° angle.
1st.) x = 5 /Sin(30°)
x = 10
!) sin(45°) = 4/x
x = 4/sin(45°)
x = 4√2
I) Cos(45°) = √3 / x
x = √3 / Cos(45°)
x = √6
E) Tan(60°) = 3√3 / x
x = 3√3 / 3
W) For isosceles right-triangle, the angle made by the legs and the hypotenuse is always 45°.
x = 45°
N) x² + x² = (7√2)²
x = 7
V) Tan(60°) = 7 / x
x = 7√3/3
K) x² + x² = (9)²
x = 9/√2
Y) Sin(60°) = 7√3/x
x = 14
M) Sin(30°) = x/11
x = 11/2
T) Sin(45°) = x/√10
x = √5
A) x + 2x + 90° = 180°
x = 30°
O) Sin(45°) = √2 / x
x = 2
R) Tan(30°) = x / 4
x = 4/√3 = 4√3 / 3
S) Sin(60°) = x / (10/3)
x = 5√3 / 3
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Related Questions
Rectangle ABCD is rotated 180°. What rule shows the input and output of the rotation, and what is the new coordinate of A′?
Answers
Which pair of equations generates graphs with the same vertex?
Answers
The pair of equations that generates graphs with the same vertex is
B) y = –4x2 and y = 4x2
What is vertex ?A vertex serves as angular point that allows the meeting of two or more lines .
To express a quadratic equation we can use :
[tex][y = a(x - h) ^{2} + k][/tex]
where vertex is (-h , k)
If we look at first option, the the vertices are [tex](-4 , 0) and (4 , 0)[/tex]
Then the second option, graphs' vertices are the same thing which is ,[tex](0 , 0).[/tex]
Therefore, the pair of equations that generates graphs with the same vertex is B) y = –4x2 and y = 4x2
CHECK THE COMPLETE QUESTION BELOW:
Which pair of equations generates graphs with the same vertex?
A) y = –(x + 4)2 and y = (x – 4)2
B) y = –4x2 and y = 4x2
C) y = –x2 – 4 and y = x2 + 4
D) y = (x – 4)2 and y = x2 + 4
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Triangles A C B and M Q R are shown. Sides A B and M R are congruent. Angles C A B and M R Q are 42 degrees. Angle C B A is 53 degrees. Angle M Q R is 85 degrees.
Are the triangles congruent? Why or why not?
Yes, all the angles of each of the triangles are acute.
Yes, they are congruent by either ASA or AAS.
No, AngleB is not congruent to AngleQ.
No, the congruent sides do not correspond.
2 triangles are connected at one side. The triangles have 2 congruent sides and 1 congruent angle. The first triangle is rotated and then translated down to form the second triangle.
Answers
By ASA postulate it can be say that the triangle ABC and triangle MRQ are congruent
What is Angle Sum Property?The sum of all three angles(interior) of a triangle is 180 degrees, and the exterior angle of a triangle measures the same as the sum of its two opposite interior angles.
Using Angle Sum Property, in ΔMRQ
<M + <R + <Q= 180
<M + 42 + 85 = 180
<M = 180 -42
<M= 53°
Now, In ΔMRQ and ΔABC
<A= <R ,
<B = <M
AB = MR
Hence, By ASA criteria ΔMRQ ≅ ΔABC
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Add the following polynomials, then place the answer in the proper location on the grid
14x^2 - 8x + 3
-6x^2 + 7x - 11
Answers
The addition of the polynomials 14x² - 8x + 3 and - 6x² + 7x - 11 is 8x² - x - 8
Polynomial(14x^2 - 8x + 3) + (-6x^2 + 7x - 11)
= 14x² - 8x + 3 - 6x² + 7x - 11
collect like terms= 14x² - 6x² - 8x + 7x + 3 - 11
= 8x² - x - 8
Therefore, the addition of the polynomials 14x² - 8x + 3 and - 6x² + 7x - 11 is 8x² - x - 8
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Miguel's coffee shop makes a blend that is a mixture of two types of coffee. Type A coffee costs Miguel $ per pound, and Type B coffee costs $ per pound. This month's blend used three times as many pounds of Type B coffee as Type A, for a total cost of $. How many pounds of Type A coffee were used
Answers
The amount of Type A coffee that was used is 40 pounds.
From the given information;
Type A coffee costs Miguel $5.95 per pound
Type B coffee costs $4.65 per pound.
For this month, the equation can be expressed as:
A + 3A
Thus;
5.95A + 3(4.65)A = 796.00
5.95A +13.95A = 796.00
19.9A = 796.00
A = 796.00/19.9
A = 40
Therefore, we can conclude that the amount of pounds of type A coffee that was used is 40 pounds.
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Please help ill give whoever answers the best the brainliest answer :))
Answers
Answer:
Step 3 is wrong and the answer should be 576
Step-by-step explanation:
Step 1 and step 2 are correct
Step 2: 4 × 12^2
You don't multiply 12 by 4, you first complete the exponent since, in PEMDAS, Exponent is before Multiplying.
Step 3 should be: 4 × (12×12)
= 4 × 144
= 576
Antonio graphs these equations and finds that the lines intersect at a single point,
(-5, 0.25).
Equation A: 4y-3x=16
Equation B: -x-8y=3
which statement is true about the values of x=-5 and y=0.25?
Answers
Option B is correct. The statement that is true about the values we have been given here is that They are the only values that make both equations true.
How to solve for the equationsWe have been given two equations
The first equation is
4y-3x=16
We have to plug in the values (-5, 0.25) in this equation
4(0.25) -3(-5) =16
Then we have
1 + 15 = 16
Hence 16 = 16 This satisfies the equation.
In the second equation we have to follow the same step
-x-8y=3
Such that
-(-5)-8*0.25 = 3
5-2 = 3
3 = 3 This also satisfies the equation.
Therefore the correct answer option is B
Complete questiona. They satisfy equation 8 but not equation A.
B. They are the only values that make both equations true.
C. They show that the equations represent the same line.
D. They satisfy equation A but not equation B.
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Gotta have answer ASAP!!!
“Tell the three ways of naming an angle”
Answers
Answer:
1 the vertex point if there are no other angles at the vertex that be confused.
2 three letters with the vertex as the center letter and the other letters representing points from each side.
3 a small number if one is given in the angle.
Answer:
Three Ways to Name an Angle:
1) By its Vertex
2) By the Three Points of the Angle (The Middle Point Must Be the Vertex)
3) By a Letter or Number Written Within the Opening of the Angle.
Step-by-step explanation:
Ten out of 50 participants scored between 65 and 75 on a test. What is the relative frequency of the class interval 65-75
Answers
The relative frequency of the class interval 65-75 is .20.
What is relative frequency?The word 'relative' is used to indicate that an event is being considered in relation or in proportion to something else.
Frequency is a way to measure how often a particular event occurs. Relative frequency, on the other hand, is a way to measure how often a particular event occurs against total occurrences.
Given that: 50 participants scored between 65 and 75 on a test.
Hence,
The relative frequency of the class interval 65-75 = 75 - 65 = 20
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8/3 + (-9/4) reduce to simplest form
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Micaela has a bat that is 30 inches long. She wants to fit it in a cube shaped box that has sides that are 17 inches. Will the bat fit? Justify your answer
Answers
The bat will not fit in the cube shaped box
How to determine if the bat will fit?The side length of the cube is given as:
x = 17
The diagonal of the cube is calculated as
[tex]d = x\sqrt 3[/tex]
So, we have:
[tex]d = 17\sqrt 3[/tex]
Evaluate
d = 29.4
29.4 is less than the length of the bat (30 inches)
This means that the bat will not fit in the cube shaped box
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(LOOK AT IMAGE)
A regular 8-sided polygon and a regular 10-sided polygon share a single side, as shown below. Calculate the size of the angle marked b. Give your answer in degrees (°).
Answers
Answer: 9
Step-by-step explanation:
The interior angle of the 8-sided polygon is
[tex]\frac{180(8-2)}{8}=135^{\circ}[/tex]
The interior angle of the 10-sided polygon is
[tex]\frac{180(10-2)}{10}=144^{\circ}[/tex]
Taking the difference, we get [tex]b=9^{\circ}[/tex]
5. The perimeter of a room is measured and found
to be 652 inches. Trim for the room is sold by
the foot. How many feet of trim must be
purchased so that the room can be trimmed?
(A) 50 ft
(B) 54 ft
(C) 55 ft
(D) 60 ft
Answers
Answer: C
Step-by-step explanation:
12in is 1 ft
652/12 is 54r4
so atlease 55
HELP HELP HELP
EASY 18 POINTS!
Solving Quadratic Equations Algebraically Explain how to determine the solutions to a quadratic equation, algebraically. Create a problem with a quadratic equation that you would solve algebraically and solve it.
Answers
Step-by-step explanation:
So a quadratic equation in factored form is generally given in the form: [tex]a(x-b)(x+c)[/tex]. Sometimes x may have a coefficient but I'll just create a simple quadratic equation. In this form it's easy to see that the solutions to the equation are b and -c, because if you input them in as x, you'll get one of the factors equal to 0, and it'll make the y-value zero, thus it's a solution. So b and c can literally be anything. But for this example I'll chose 3 and 6 to keep it simple. Inputting these as b and c you'll get: [tex]a(x-3)(x+6)[/tex]. Now the value of a will determine the stretch/compression, but to keep it really simple I'll just say that a=1. So now all you have to do is expand the two factors. When you expand them you'll get it in the form: [tex](x-b)(x+c) = x^2+cx-bx-bc[/tex] by using the foil method. So if you expand the two factors in this example you'll get: [tex]x^2+6x-3x-18[/tex] which simplifies to [tex]x^2+3x-18[/tex]. So cool now we have our equation. Now it's time to solve it, you can either factor it (since you literally just had it in factored form), or use the quadratic formula I'll show both methods
Factoring:
When you factor an equation in the form: [tex]ax^2+bx+c[/tex]. You usually multiply the coefficients a and c. Then you'll find factors of ac that add up to b. In this example ac is really just c because a is 1...
So given the equation: [tex]x^2+3x-18[/tex] You want to look for factors of -18 that add up to 3. And whenever you have a negative number as AC you really want to look for factors that have a distance of b which in this case is 3. For example I would say that 9 and 3 have a distance of 6. And then after that depending on whether b is negative or positive. I can choose which factor will be negative and which will be positive. If b was 6 well then 9 would have to be positive and 3 would be negative, but if b was -6 then 9 would have to be negative and 3 would have to be positive.
So in this example look for factors that have "distance" of 3. Well 6 and 3 have a "distance" of 6 so I know those 2 will be the factors. Since 3 is positive that means 6 will be positive, and 3 will be negative. so they add up to 3 and multiply to get -18
AC factors that add up to 3 and multiply to -18: 6 and -3
Now write it in factored form using the two factors:
[tex](x-3)(x+6)[/tex]
Now set up each factor equal to 0 and solve for x:
[tex]x-3 = 0\\x=3[/tex]
[tex]x+6=0\\x=-6[/tex]
This gives you the two solutions: x=3 and x=-6
Quadratic Formula:
The quadratic formula is usually used when a equation can't be easily factored. The quadratic formula gives both zeroes in the equation: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]. Notice the plus or minus sign next to the square root? That's where the the two solutions will come from, or possibly one solution if it's at the vertex. or maybe even no real solutions if the quadratic never intersects the x-axis.
Ok so let's identify a, b, and c. We're given the equation: [tex]x^2+3x-18[/tex]. so a=1, b=3, and c=-18. Plugging these values into the equation you get:
[tex]x=\frac{-(3)\pm\sqrt{(3)^2-4(1)(-18)}}{2(1)}\\[/tex]
Simplifying it a bit gets you the equation:
[tex]x=\frac{-3\pm\sqrt{81}}{2}[/tex]
Simplifying the radical gives you:
[tex]x=\frac{-3\pm9}{2}[/tex]
Use the positive sign:
[tex]x=\frac{-3+9}{2}\\x=\frac{6}{2}\\x=3[/tex]
Use the negative sign:
[tex]x=\frac{-3-9}{2}\\x=\frac{-12}{2}\\x=-6[/tex]
This gives you the two solutions x=3, and x=-6
Find the area of the trapezoid
Answers
Answer:
294.84 ft²
Step-by-step explanation:
A = (B + b)h/2
A = (28.5 ft + 18.3 ft)(12.6 ft)/2
A = 294.84 ft²
Answer: 294.84 ft^2
Step-by-step explanation:
Area of trapezoid=((a+b)/2)*h
here
a=28.5 ft
b=18.3 ft
h=12.7 ft
Area=((28.5+18.3)/2)*(12.7)
Area=294.84 ft^2
Which compound inequality is represented by the graph?
←
-5-4-3-2-1 0 1 2 3 4 5
O-3
O-3 < x≤1
O x≤-3 or x>1
Ox<-3 or x ≥ 1
Answers
The compound inequality represented by the graph shown in the image below is 5 < x < 9
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The image shown represents a compound inequality. It represents:
x > 5 and x < 9
The compound inequality represented by the graph shown in the image below is 5 < x < 9
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What QUANTITY does 25.0 m represent?
length
millimeters
meters
milliliters
Answers
Answer:
Step-by-step explanation:
m represents the meters.
If n(A) equals 100 and n(B) is equals to 120 and A is the subset of B, find the value of an n(A union B)
Answers
Answer:
200
Step-by-step explanation:
Solution,
Given,
n(A)=100
n(B)=120
A⊂B
n(A∩B)=20
n(A∪B)=n(A)+n(B)-n(A∩B)
n(A∪B)=100+120-20
n(A∪B)=200
n(A union B) is equal to the number of elements in set B, which is 120.
How to find n(A union B)If A is a subset of B, it means that every element in set A is also an element of set B.
In this case, n(A) represents the number of elements in set A, which is 100, and n(B) represents the number of elements in set B, which is 120.
To find the value of n(A union B) (the number of elements in the union of sets A and B), we need to consider that the union of two sets includes all the elements that are in either set A or set B, or both.
Since A is a subset of B, all the elements in set A are already included in set B. Therefore, the union of sets A and B will be equal to set B itself.
Thus, n(A union B) is equal to the number of elements in set B, which is 120.
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Verbal
4. Are one-to-one functions either always increasing or
always decreasing? Why or why not?
Answers
Answer:
If a function is continuous and one - to - one then it is either always increasing or always decreasing.
Step-by-step explanation:
An easy way to see this on a graph is to draw a horizontal line through the graph . If the line only cuts the curve once then the function is one - to - one.
Answer:
If a one-to-one function is not continuous, it is sometimes increasing or decreasing. If a one-one function is continuous, it is always increasing or always decreasing.
For example, if [tex]$f(x)=\left\{\begin{array}{lll}-x & \text { if } & |x| \geq 1 \\ x & \text { if } & |x| < 1\end{array}\right.$[/tex]
This function is one-to-one and it is not always increasing or decreasing.
Step-by-step explanation:
A statement that are one-to-one functions either always increasing or always decreasing is given.
It is required to explain the given condition.
To explain the given condition, consider a continuous and a not continuous function then explain about the one-to-one function.
If a one-to-one function is not continuous, it is sometimes increasing or decreasing.
For example, if [tex]$f(x)=\left\{\begin{array}{lll}-x & \text { if } & |x| \geq 1 \\ x & \text { if } & |x| < 1\end{array}\right.$[/tex]
This function is one-to-one and it is not always increasing or decreasing.
If a one-one function is continuous, it is always increasing or always decreasing.
For example, if f(x)=x-3. It is a continuous function and it reaches a minimum value at some values of x and it then keeps increasing.
There will be the same output value for different input values. It does not pass the horizontal line test and so it is not a one-to-one function.
how many moles of sucrose (C12 H22 O11) would be in 8.7 L of a 1.1 M solution of sucrose
Answers
Answer:
9.57 moles
Step-by-step explanation:
There is 1.1 mole per liter....
1.1 M/ l * 8.7 L = 9.57 moles
The triangles are similar. If WZ = 15, ZY = 12, and XY = 11, find WV. Round to the nearest tenth.
Answers
Answer:
13.8
Step-by-step explanation:
because they're similar, we know that
zy ÷ wz has the same ratio as xy ÷ wv
12 / 15 = 11 / wv
cross multiply
12wv = 165
÷ 12 ÷12
wv = 13.75
13.75 rounded to nearest tenth is 13.8
Of the 500 sample households, 7 had three or more large-screen TVs. Among the sample households, 121 had no car, 172 had one car, and 207 had two or more cars. Estimate the percentage of households in the town with one or more cars; attach a standard error to the estimate. If this is not possible, explain why not.
Answers
Hence, The percentage of households in the town with one or more cars = 75.8%, a standard error to the estimate= 1.92%
Total sample households = 500
Households in the town with one car = 172
Households in town with two or more cars =207
Households in the town with one or more cars = 172 + 207
= 379
The percentage of households in the town with one or more cars =
(379 / 500)*100 = 75.8%.
A standard error to the estimate = 1.92%.
Hence, The percentage of households in the town with one or more cars = 75. , a standard error to the estimate= 1.92%
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Farmers Jay, Peter and Sam own rectangular farms, as indicated in the figure. Jay owns 2 acres of land, Peter owns 4 acres and sam owns 6 acres. Find the areo of the comman pasture
Answers
The area or the common pasture will be 12 acres.
How to calculate the area?Based on the information given, the formula to use will be:
ab/ac = 2/4
b/c = 1/2 .... i
Also, ab/bd = 2/6
a/d = 1/3 .... ii
Multiply both equation
1/2 × 1/3 = 1/6
Therefore, the area will be
= 6 × 2
= 12 acres
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Find the equivalent expression of the following: x3 (x2 + 5x + 7)
x5 + 5x3 + 7x2
x6 + 5x4 + 7x3
x5 + 4x4 + x4 + 8x3 – x3
x5 + 3x4 + x4 + 6x3 + x3
Answers
The equivalent expression of x^3 (x^2 + 5x + 7) is x^5 + 4x^4 + x^4 + 8x^3 - x^3
How to determine the equivalent expression?The expression is given as:
x^3 (x^2 + 5x + 7)
Expand the expression
x^3 * x^2 + x^3 * 5x + x^3 * 7
Evaluate the product
x^5 + 5x^4 + 7x^3
Expand the expression
x^5 + 4x^4 + x^4 + 8x^3 - x^3
Hence, the equivalent expression of x^3 (x^2 + 5x + 7) is x^5 + 4x^4 + x^4 + 8x^3 - x^3
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Find the Greatest Common Factor of Two or More Expressions
In the following exercises, find the greatest common factor.
1. 8,18
Answers
Answer:
The GCF is 2.
Step-by-step explanation:
In my opinion, one of the easier ways to find the greatest common factor of two numbers is to get the prime factors of both and multiply the common ones. The prime factorization of 8 is 2*2*2, and the prime factorization of 162 is 2*3*3 (you can make a factor tree for both of these numbers to verify this). The only common prime factor for both of these numbers is 2, which means the greatest common factor of 8 and 18 is 2.
3a
From the information given, determine which triangles, if any, are
congruent and state by which rule. If the triangles cannot be shown
to be congruent, write, "Cannot be determined" and explain.
Answers
Answer: [tex]\triangle COA \cong \triangle DOB[/tex] by the rule ASA
Step-by-step explanation:
[tex]\overline{CO} \cong \overline{OD}[/tex] (given)
[tex]\angle ACO \cong \angle ODB[/tex] (given)
[tex]\angle COA \cong \angle BOD[/tex] (vertical angles)
So, [tex]\triangle COA \cong \triangle DOB[/tex] by the rule ASA.
Mary wants to fence in a rectangular run for her dogs. She has decided that the run will be 5 yards wide. A rectangle with a width of 5 yards and height of x. Which statement best describes the possible lengths of the run if she can use no more than 40 yards of fencing? at most 8 yards at most 15 yards more than 8 yards more than 15 yards Mark this and return
Answers
The length of the run is at most 15 yards
How to determine the true statement?The given parameters are:
Width = 5 yards
Height = x
Perimeter = Not more than 40 yards
The perimeter is calculated as:
P = 2 *(Width + Height)
So, we have:
2 *(5 + x) ≤40
Divide by 2
5 + x ≤ 20
Subtract 5 from both sides
x ≤ 15
This implies that the length of the run is at most 15 yards
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What is the relationship between a and b?
answer may also be none of the above
Answers
Answer:
Supplementary angles
Step-by-step explanation:
The two angles combined form a line and their measures add to 180°.
Answer: Supplementary angles
Need help with this geometry question.
Answers
Answer:
x = 80
Step-by-step explanation:
if ray RU bisects <QRS that means it divided the angle into two equal parts
then we can write the following equation to find the value of x:
<SRU = <QRU
50 = (x/2 + 10) subtract 10 from both sides
40 = x/2 multiply both sides with 2
80 = x
<QRS = 100 because it's the sum of <SRU and <QRU
the table shows a proportional relationship between the distance a snall travels and the time it takes what is the proportional constant in centimeters per minute
Answers
The constant of proportionality in centimeters per minute is: 5.5.
How to Find the Constant of Proportionality?To find the constant of proportionality of the table shown in the image attached below, use one pair of points, (12, 66).
Constant of proportionality, k = y/x, therefore, the proportional constant in centimeters per minute would be:
k = 66/12 = 5.5 cm per min.
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